{"id":1613,"date":"2012-05-18T06:32:32","date_gmt":"2012-05-18T06:32:32","guid":{"rendered":"http:\/\/www.SchoolTutoring.com\/help\/?p=1613"},"modified":"2014-12-02T08:33:44","modified_gmt":"2014-12-02T08:33:44","slug":"transpose-of-a-matrix","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/transpose-of-a-matrix\/","title":{"rendered":"Transpose of a Matrix"},"content":{"rendered":"<p>Transpose of a matrix is the matrix obtained by changing its rows into corresponding columns or columns into corresponding rows. The transpose of a <em>m<\/em> \u00d7 <em>n<\/em> matrix is a <em>n<\/em> \u00d7 <em>m<\/em> matrix that results by interchanging the rows and columns of the matrix. The transpose of a matrix is written with the superscript T or &#8216;.<\/p>\n<p><a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1614\" title=\"transpose\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose.png\" alt=\"\" width=\"326\" height=\"85\" srcset=\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose.png 326w, https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose-300x78.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Example,<\/p>\n<p><a href=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose-example.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1615\" title=\"transpose example\" src=\"https:\/\/www.SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose-example.png\" alt=\"\" width=\"333\" height=\"85\" srcset=\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose-example.png 333w, https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2012\/05\/transpose-example-300x76.png 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Properties<\/strong><\/p>\n<ul>\n<li>The transpose of the transpose of a matrix is the matrix itself.<\/li>\n<\/ul>\n<p>(A<sup>T<\/sup>)<sup>T<\/sup>= A<\/p>\n<ul>\n<li>The transpose of a matrix times a scalar is equal to the scalar times the transpose of the matrix.<\/li>\n<\/ul>\n<p>(kA)<sup>T<\/sup> = kA<sup>T<\/sup><\/p>\n<ul>\n<li>The transpose of the sum of two matrices is equivalent to the sum of their transposes.<\/li>\n<\/ul>\n<p>(A + B)<sup>T<\/sup> = A<sup>T<\/sup> + B<sup>T<\/sup><\/p>\n<p>The transpose of the product of two matrices is equivalent to the product of their transposes in reversed.<\/p>\n<p>(A \u00d7 B)<sup>T<\/sup> = B<sup>T<\/sup> \u00d7 A<sup>T<\/sup><\/p>\n<p>SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Keswick visit: <a href=\"..\/..\/tutoring-in-keswick-ontario\">Tutoring in Keswick.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Transpose of a matrix is the matrix obtained by changing its rows into corresponding columns or columns into corresponding rows. The transpose of a m \u00d7 n matrix is a n \u00d7 m matrix that results by interchanging the rows and columns of the matrix. The transpose of a matrix is written with the superscript [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[14],"tags":[1417,1848],"class_list":["post-1613","post","type-post","status-publish","format-standard","hentry","category-pre-calculus","tag-propertiesofatransposeofamatrix","tag-transposeofamatrix"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1613","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=1613"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1613\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=1613"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=1613"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=1613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}